In MIMO OFDMA cellular systems, such as 3GPP LTE or IEEE 802.16e/m, closed-loop MIMO precoding is defined to enable high throughput downlink transmissions to fixed and nomadic users. Feedback information is obtained at the transmitter via the report a precoding matrix index (PMI) from a receiver to a transmitter. This PMI is used to represent a matrix in a codebook (a set of matrices), and it is used at the transmitter to derive a downlink precoder.
Simple codebook structures are used in the first generation of MIMO OFDMA systems, such that the PMI can be represented with a few bits. Small codebooks achieve a coarse quantization of the spatial channel. For example in 3GPP LTE Release 8, a 4-bit codebook is defined and the 4-bit PMI can be reported via a capacity-limited feedback channel called PUCCH [1, 2]. Precoding matrices are defined for each possible transmission rank, which determines the size of the precoding matrix. The overall codebook is a set of matrices for each rank. The feedback of the PMI thus consists of a rank indication (RI) and a PMI for the codebook subset of the given rank RI. Since the rank of the propagation channel varies slowly in comparison with fast fading over which the PMI is adapted, the rank indication is reported with a longer period than the PMI.
More importantly, since the rank indication remains valid during several reports of the PMI, it must be encoded with a better error protection code in order to ensure that consecutive PMI reports are not invalidated by one erroneous RI report. In general, this is naturally ensured by the fact that the rank can take values in a limited range, such as {1, 2, 3, 4} in LTE Rel-8, due to the limitation to a maximum of 4 antennas at the transmitter and 4 antennas at the receiver. Thus the RI can be represented by 2 bits. Since the PMI is in general reported along with a channel quality indication (CQI) that represents the channel quality assuming transmit precoding with the reported PMI, the total size of the feedback message that contains the PMI+CQI is larger than the 4 bits used to represent just the PMI. The message size will be 8 to 11 bits with one to two CQIs, respectively, in LTE Rel-8. The PUCCH being transmitted in a fixed-size time-frequency resource with a fixed modulation, the 2 bits of RI that are reported individually are naturally better protected than the 8 or 11 bits of PMI+CQI that are jointly reported, since the 2 bits of RI enjoy a lower error-correction encoding rate.
Enhancements of the feedback for closed-loop precoding beyond the simple 4-bit codebook or for larger transmit antenna array sizes would require more complex codebook structures, as well as a larger codebook size. Naturally, the feedback mechanisms should be designed accordingly, in order to take advantage of enhanced codebook properties, and to ensure smooth operation of the feedback in order to avoid disrupting propagation of feedback errors. It can be easily understood that increasing the size of the PMI without changing the reporting mechanisms could lead to situation where a very large PMI would lead to a very large feedback message, which would often be received in error. In order to cope with this situation, it would be desirable to better balance the feedback load between the RI and PMI+CQI reports. Moreover, the PUCCH design in LTE Rel-8 can accommodate a maximum of 13 information bits. If the size of the PMI was increased beyond 6 bits, one would either need to entirely re-design the feedback channel or increase the information load of the RI report. In would also be desirable to maintain the possibility of the existing system operation while allowing the operation of the advanced reporting format, based on the same feedback channel physical structure.
A first type of enhanced codebook contains matrices that provide a quantization of the MIMO propagation channel between an array of transmitting antennas and an array of receiving antennas. Due to the wide range of deployed transmit antenna arrays, such a codebook should effectively quantize single-polarized channels as well as dual-polarized channels. This type of codebook naturally contains one set of matrices that quantize the single-polarized space, and a second set of matrices that quantize the dual-polarized space, as shown in FIG. 1. Note that these two sets may have common elements. An example of such a codebook can be found in 3GPP LTE Rel-8 specifications [1].
Another example of such a codebook is given in [3], where the matrices take the form:W=WMI1(1)WMI2(2) 
The inner precoder WMI1(1) has a block diagonal structure
      W          MI      ⁢                          ⁢      1              (      1      )        =      [                                                      W              ~                                      MI              ⁢                                                          ⁢              1                                      (              1              )                                                0                                      0                                                    W              ~                                      MI              ⁢                                                          ⁢              1                                      (              1              )                                            ]  
For rank 1, the precoder could be formed as
      W    =                  [                                                                              W                  ~                                                  MI                  ⁢                                                                          ⁢                  1                                                  (                  1                  )                                                                    0                                                          0                                                                        W                  ~                                                  MI                  ⁢                                                                          ⁢                  1                                                  (                  1                  )                                                                    ]            ⁡              [                                            1                                                          α                                      ]              ,      α    ∈          {              1        ,                  -          1                ,        j        ,                  -          j                    }      
The rank 2 case would follow similarly as
      W    =                  [                                                                              W                  ~                                                  MI                  ⁢                                                                          ⁢                  1                                                  (                  1                  )                                                                    0                                                          0                                                                        W                  ~                                                  MI                  ⁢                                                                          ⁢                  1                                                  (                  1                  )                                                                    ]            ⁡              [                                            1                                      1                                                          α                                                      -                α                                                    ]              ,      α    ∈          {              1        ,        j            }      
The second precoder represents a co-phasing factor that takes care of short-term channel variations and can be made to adjust the structure of the overall precoder W to match either a single-polarized linear uniform array (ULA) or a cross-polarized array at the transmitter.
There is therefore a need in the art for efficient techniques for adapting the feedback rate in capacity-limited channels for reporting channel state information with codebook-based quantization, which is proposed in this disclosure.